This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

More Children and Plants

Stage: 2 and 3 Challenge Level:

This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.) It is seen as a possible follow-on fromPlants.

In "Plants" we had three children sharing $10$ plants in the three overlapping circles.

This particular challenge is about extending that, so that we consider four and then maybe five children in a similar way.

In considering these larger numbers we have to examine a different arrangement of the circles (possibly changed into slightly different shapes).

You will need to draw these four (first of all) areas in such a way that there is a section for each of the sharing situations. In the case of plants there were seven sections - allowing for each child to have an overlapping part with each and all of the other children.

Once you have drawn an arrangement for four areas I suggest that you start with allocating $4, 5, 6, 7$ to the areas.

As before, where can a certain number of plants go? I suggest you start with a number like $19$ for the total number plants.

Find all the answers that satisfy the requirements of having $4, 5, 6, 7$ shared in the different regions using $19$ plants.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.